A general method for solving constrained optimization problems (Q1058991)

A general problem of constrained minimization is studied. The minima are determined by searching for the asymptotical values of the solutions of a suitable system of ordinary differential equations. For this system, if the initial point is feasible, then any trajectory is always inside the set of constraints and tends towards a set of critical points. Each critical point that is not a relative minimum is unstable. For formulas of one-step numerical integration, an estimate of the step of integration is given, so that the above mentioned qualitative properties of the system of ordinary differential equations are kept.